{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/3_First_order_methods/3_1_Introduction.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8Up3mCZxYKUT"
   },
   "source": [
    "## Chapter 3: First order methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gBg2AmauYKUU"
   },
   "source": [
    "# 3.1 Introduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "38t1N8goYKUV",
    "outputId": "61a33352-bd22-43f1-d4c2-7feed8c9e812"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "Cloning into 'chapter_3_images'...\n",
      "done.\n"
     ]
    }
   ],
   "source": [
    "# import standard libs\n",
    "import os\n",
    "\n",
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone images\n",
    "if not Path('chapter_3_images').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/3_First_order_methods/chapter_3_images\n",
    "else:\n",
    "    print('chapter_3_images already cloned!')\n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_3_images') \n",
    "\n",
    "# image paths\n",
    "image_path_1 = 'chapter_3_images/Fig_2_7.png'\n",
    "\n",
    "# standard imports\n",
    "from IPython.display import Image, HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "I2WOGMdXYKUW"
   },
   "source": [
    "In the previous Chapter we introduced zero order optimization methods - including global and local optimization schemes.  The latter methods were by far the most promising, where we repeatedly refined an initial sample input by traveling in *descent directions*, i.e., directions in the input space that lead to points lower and lower on the function.  There we described zero-order methods for finding such descent directions at each step.  These consist of various brute-force search approaches that are either prohibitively expensive to employ for functions of even moderately large input dimension (e.g., random search) or are severely restricted in terms of the quality of descent directions they can find (e.g., coordinate search)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xmJLJb2GYKUW"
   },
   "source": [
    "In this Chapter we mirror the structure of our discussion in the previous Chapter in describing *first order optimization methods*.  We begin with a discussion of the *first order optimality condition* - which codifies how the first derivative(s) of a function characterize its minima.  Then we discuss some fundamental concepts related to the geometric nature of (tangent) hyperplanes and in particular the first order Taylor series in preparation for discussing the *gradient descent algorithm*, a hugely popular first order local optimization algorithm.  As we will see, by exploiting a function's first order information we can construct a first order local optimization method that naturally determines high quality descent directions at a cost that is cheaper than even the coordinate search approach described in the last Chapter.  \n",
    "\n",
    "With these ideas in hand we can then formally detail the gradient descent algorithm, examining a number of examples that help exhibit the algorithm's general behavior.  As with any local optimization method, here we must too worry about the selection of the steplength parameter.  However because we will now be leveraging first order derivative(s) in constructing each descent direction we can say much more - mathematically speaking - about how to rigorously set the steplength parameter for gradient descent.  Finally we will also discuss first order coordinate approaches, which among other things allow us to make more direct use of the first order optimality conditions themselves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "82mkDgKyYKUX"
   },
   "source": [
    "## Big picture view of the gradient descent algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zJA3a_O7YKUX"
   },
   "source": [
    "As we saw previously, a local optimization method is one where we aim to find minima of a given function by beginning at some point $\\mathbf{w}^0$ and taking number of steps $\\mathbf{w}^1, \\mathbf{w}^2, \\mathbf{w}^3,...,\\mathbf{w}^{K}$ of the generic form \n",
    "\n",
    "$$\n",
    "\\mathbf{w}^{\\,k} = \\mathbf{w}^{\\,k-1} + \\alpha \\mathbf{d}^{\\,k}.\n",
    "$$\n",
    "\n",
    "where $\\mathbf{d}^{\\,k}$ are direction vectors (which ideally are *descent directions* that lead us to lower and lower parts of a function) and $\\alpha$ is called the *steplength* parameter.  We saw how the random / coordinate search algorithms follows this framework precisely, the only difference between the two being how a descent direction is found at each step.  This idea - how a descent direction is found / computed - is what distinguishes any two local methods from one another.  One of the ultimate aims of this Chapter is to introduce the *gradient descent algorithm*, which is a *first order* local optimization method as it employs a function's first derivative(s) to cheaply compute a high quality descent direction.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VwMPB_5OYKUY"
   },
   "source": [
    "Here is how the gradient descent algorithm works at a high level (we will see complete details in the Chapter itself).  The first derivative of a function helps form the best *linear* approximation to the function locally (called the *first order Taylor series approximation*).  Because this approximation matches the function locally - and because it is extremely easy to compute the descent direction of a line or hyperplane regardless of its dimension (as we will see in this Chapter) - the descent direction of the tangent hyperplane is also a descent direction for the function itself.  If we simply steal this descent direction at each step and employ it in a local optimization framework we have created the *gradient descent algorithm*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "id": "WH79Xh8dYdgr",
    "outputId": "c277779b-d8fc-444b-d9ad-37b52ef4d565"
   },
   "outputs": [
    {
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     },
     "execution_count": 2,
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    }
   ],
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    "Image(image_path_1, width=600)"
   ]
  },
  {
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   "metadata": {
    "id": "8DrBKfbsYKUZ"
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    "<figure>\n",
    "<figcaption>   \n",
    "<strong>Figure 1:</strong> <em> A figurative drawing of the gradient descent algorithm.  The first order Taylor series approximation provides an excellent and easily computed descent direction at each step of this local method of optimization (here a number of approximations are shown in green).   Employing these directions at each step the *gradient descent algorithm* can be used to properly minimize generic functions.  Moreover, unlike the zero-order local search algorithms, gradient descent scales very well with input dimension since the descent direction of a hyperplane is much more easily computed in high dimensions than any search approach.\n",
    "</em>  </figcaption> \n",
    "</figure>"
   ]
  }
 ],
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    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false,
   "widenNotebook": false
  }
 },
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 "nbformat_minor": 1
}
